Propagation of shock wave in a non-ideal dusty gas in rotating medium using Lie group theoretic method: Isothermal flow

Abstract

This paper concerns with the similarity solutions using Lie group theoretic method for one-dimensional unsteady isothermal flow behind the shock wave in the mixture of non-ideal gas and small solid particles in rotating medium. Group theoretic technique brings the different possible cases of potential solutions with the power law, particular case of power law and exponential law shock paths with the different choices of constants present in the generators of the Lie group of transformations. Similarity solutions for non-ideal dusty gas (a mixture of non-ideal gas and small solid dust particles) exist if the density of the ambient medium is constant. Solutions are obtained for both exponential law and power law shock paths. The effects of the variation of the physical parameters on the flow variables distribution behind the shock wave front, and on the shock are discussed. The shock strength increases with an increase in the ratio of the specific heat of the solid particles to the specific heat of the gas at constant volume [Formula: see text], the initial azimuthal velocity variation index [Formula: see text], and the ratio of the density of solid particles to the initial density of the gas [Formula: see text]. The shock wave decays with an increase in the value of gas non-idealness parameter [Formula: see text].